of two lines which meet
each other, and do not lie straight with respect to each other (see
GEOMETRY, EUCLIDEAN). According to Proclus an angle must be either
a quality or a quantity, or a relationship. The first concept was
utilized by Eudemus, who regarded an angle as a deviation from a
straight line; the second by Carpus of Antioch, who regarded it as the
interval or space between the intersecting lines; Euclid adopted the
third concept, although his definitions of right, acute, and obtuse
angles are certainly quantitative. A discussion of these concepts and
the various definitions of angles in Euclidean geometry is to be
found in W.B. Frankland, _The First Book of Euclid's Elements_ (1905).
Following Euclid, a right angle is formed by a straight line standing
upon another straight line so as to make the adjacent angles equal;
any angle less than a right angle is termed an acute angle, and any
angle greater than a right angle an obtuse angle. The difference
between an acute angle and a right angle is termed the complement of
the angle, and between an angle and two right angles the supplement
of the angle. The generalized view of angles and their measurement is
treated in the article TRIGONOMETRY. A solid angle is definable as
the space contained by three or more planes intersecting in a common
point; it is familiarly represented by a corner. The angle between two
planes is termed dihedral, between three trihedral, between any number
more than three polyhedral. A spherical angle is a particular dihedral
angle; it is the angle between two intersecting arcs on a sphere, and
is measured by the angle between the planes containing the arcs and
the centre of the sphere.

[v.02 p.0015]

The angle between a line and a curve (mixed angle) or between two
curves (curvilinear angle) is measured by the angle between the line
and the tangent at the point of intersection, or between the tangents
to both curves at their common point. Various names (now rarely, if
ever, used) have been given to particular cases:--amphicyrtic (Gr.
[Greek: amphi], on both sides, [Greek: kyrtos], convex) or cissoidal
(Gr. [Greek: kissos], ivy), biconvex; xystroidal or sistroidal (Gr.
[Greek: xystris], a tool for scraping), concavo-convex; amphicoelic
(Gr. [Greek: koilae], a hollow) or _angulus lunularis_, biconcave.

[Illustration: The Angler (_Lophius piscatorius_).]

ANGLER, also sometimes called fishing-frog, frog-fish, sea-devil
(_Lophius pi